Efficiency Analysis of Publicly Owned Power Distribution Companies in the US

Publicly owned electricity distributors operate under a different incentive structure than private utilities: they cannot simply exit loss-making service areas and their mandate is to ensure universal access rather than to maximise returns. This makes efficiency benchmarking both more important and methodologically more demanding — standard profit-based metrics are not applicable, and efficiency has to be assessed against a production frontier constructed from peers operating under the same constraints.

This project benchmarks 130 publicly owned US electricity distribution companies using three complementary frontier methods: Data Envelopment Analysis (DEA), Corrected Ordinary Least Squares (COLS), and Stochastic Frontier Analysis (SFA). Each method makes different assumptions about the source of deviation from the efficiency frontier, and comparing their results reveals what is structural inefficiency versus what is noise.

Model specification

The production process of an electricity distributor is defined by one input and two outputs:

• Input: Operational Expenditure (OPEX)
• Outputs: Units of electricity distributed (GWh) and Length of supply lines operated (000s km)

Two candidate variables — overhead share percentage (Ovshare) and network intensity (Intensity) — were assessed for inclusion. Ovshare is a percentage and not suitable for DEA model inputs. Intensity showed near-zero correlation (0.0065) with OPEX and was dropped to avoid unnecessary model complexity. Ovshare's correlation with OPEX was also negligible at 0.05.

A Translog functional form was selected for the parametric models. Eight candidate models were tested; Model 8 (the full Translog specification) was chosen based on post-estimation diagnostics:

• White's test: p > 0.05 — no heteroskedasticity
• Ramsey RESET test: p > 0.05 (both with and without multicollinear variables) — no omitted variable bias or misspecification
• Multicollinearity among second-order Translog terms is expected and does not invalidate the model

DEA model selection

The input-oriented VRS (Variable Returns to Scale) DEA model was chosen over CRS (Constant Returns to Scale) for two reasons. First, publicly owned distributors cannot freely control their output volumes — they are obligated to supply electricity to all customers in their service territory. Cost reduction (the input) is the controllable lever. Second, avplots from the Translog model showed negative slopes on second-order terms, indicating increasing returns to scale — which makes the VRS frontier the appropriate benchmark.

DEA was implemented in PIM-DEA. Input: OPEX. Outputs: Units, Length.

DEA results

CRS produces a lower mean and lower standard deviation than VRS. This is expected: CRS folds scale inefficiency into technical inefficiency, dragging down scores for companies that are technically efficient at their operating scale but not at the most productive scale size (MPSS).

Two companies were examined in detail. Company 22 achieved 100% efficiency under both VRS and CRS — it is operating at the MPSS with no scale inefficiency. Company 23 achieved 47.6% VRS efficiency and 46.3% CRS efficiency, with a scale efficiency of 97% (CRS/VRS ratio). Despite scale efficiency being close to 1, Company 23 is operating under decreasing returns to scale and would need to reduce its OPEX from 160.9 to 76.6 (VRS target) or 74.4 (CRS target) to reach the frontier, while scaling down Units from 24.1 to 21.3 GWh and Length from 35.2 to 31.1 (000s km) to reach MPSS. Company 23's peer set in VRS includes Companies 22, 46, and 57, weighted at 42%, 27%, and 31% respectively.

Deterministic frontiers: COLS and MOLS

Using Model 8, the Translog cost function was estimated and the frontier shifted downward by the minimum residual to produce COLS (Corrected OLS) efficiency scores. COLS assumes that all deviation above the frontier represents inefficiency. Mean COLS cost efficiency was 77.3%, with a minimum of 55.6% and a maximum of 100% (99th percentile only).

MOLS (Modified OLS) relaxes the assumption slightly by using the mean residual shift rather than the minimum, producing less extreme efficiency estimates that may better reflect reality when some deviation from the cost frontier is attributable to factors outside managerial control.

Stochastic Frontier Analysis

COLS and MOLS attribute all upward deviation from the cost frontier to inefficiency. SFA decomposes residuals into an inefficiency component and a random noise component. This distinction is economically meaningful for electricity distributors: companies serving hurricane-prone regions face higher maintenance OPEX; those operating across desert terrain face higher line failure rates. These cost drivers are not evidence of managerial inefficiency — they are environmental factors that any well-managed company in that geography would face.

The kernel density of residuals showed a rightward skew, consistent with the presence of an inefficiency term. SFA was estimated using the Translog Model 8, with the sample of 130 companies sufficient for reliable SFA estimation. Results showed that accounting for noise meaningfully changes efficiency rankings relative to COLS — companies in high-risk geographic environments move upward when random noise is separated from inefficiency.

Technical notes

DEA was run in PIM-DEA with input orientation, VRS and CRS specifications, and peer identification for target-setting. All parametric models (Translog OLS, COLS, MOLS, SFA) were estimated in Stata. Post-estimation diagnostics — heteroskedasticity tests, Ramsey RESET, avplots, VIF — were run in Stata. Robust standard errors were used throughout. The dataset contains 130 publicly owned US electricity distribution companies.